#14990: Implement algebraic closures of finite fields
-------------------------------------------------+-------------------------
Reporter: pbruin | Owner:
Type: enhancement | Status:
Priority: major | needs_review
Component: algebra | Milestone: sage-5.13
Keywords: finite field algebraic | Resolution:
closure | Merged in:
Authors: Peter Bruin | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
Dependencies: #14958, #13214 | Stopgaps:
-------------------------------------------------+-------------------------
Comment (by vdelecroix):
Hi,
Thanks for the nice patch! I played a little bit with the patch and here
are few comments (from a user point of vue).
For the `FiniteFieldAlgebraicClosure`
- the method .cardinality() fails
- .some_elements() returns a very stupid list
- .gens() is not happy. I guess we can return a `Family`. The problem is
that in the specification it is written that the method should return a
tuple.
For elements
- many methods can be implemented in two lines as
{{{
def my_method(self):
return self._value.my_method()
}}}
this concerns `minimal_polynomial`, `trace`, `norm`,
`multiplicative_order`, ...
- in a similar way (calling apropriate method of _value and applying a
morphism) it is straightforward to implement `frobenius`, `pth_power`,
`pth_root`, ...
- to mimic AA or QQbar I would like a method
``as_finite_field_element(self, minimal=False)`` which return a triple
(finite_field, value, homomorphism)
Vincent
--
Ticket URL: <http://trac.sagemath.org/ticket/14990#comment:9>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
--
You received this message because you are subscribed to the Google Groups
"sage-trac" group.
To unsubscribe from this group and stop receiving emails from it, send an email
to [email protected].
To post to this group, send email to [email protected].
Visit this group at http://groups.google.com/group/sage-trac.
For more options, visit https://groups.google.com/groups/opt_out.
